Pleas help with this. Explain the steps so I can understand what I am doing.
solve
0.3x + 9<_ 0.7x -8
the solution is {x|x ? ? }
_ this line is suppose to go under the 9 but I don't know how on computer do you?
You will need to solve it like an equation, by keep the inequality sign.
The less than or equal to sign can be written as "& l e ;" without the quotes and the intevening spaces.
- Group like terms on same side of inequality sign
- reduce to one term on each side
- divide each side by the coefficient of the unknown, flip the direction of inequality if the coefficient is negative.
To solve the inequality 0.3x + 9 ≤ 0.7x - 8, we'll follow these steps:
Step 1: Move all terms containing x to one side of the inequality and constants to the other side.
Start by subtracting 9 from both sides of the inequality:
0.3x ≤ 0.7x - 8 - 9
Simplifying the right side of the equation gives us:
0.3x ≤ 0.7x - 17
Step 2: Simplify the equation by combining like terms.
To do this, subtract 0.7x from both sides of the inequality:
0.3x - 0.7x ≤ 0.7x - 0.7x - 17
This results in:
-0.4x ≤ -17
Step 3: Multiply or divide (if the coefficient is negative) both sides of the inequality by the coefficient of x to isolate x.
Since the coefficient of x is -0.4, divide both sides of the equation by -0.4. However, when dividing by a negative number, remember to reverse the inequality sign:
-0.4x / -0.4 ≥ -17 / -0.4
Simplifying gives us:
x ≥ 42.5
The solution to the inequality is {x | x ≥ 42.5}. This means that any value of x that is greater than or equal to 42.5 will satisfy the inequality.